# On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary

@article{Doikou2005OnQG, title={On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary}, author={Anastasia Doikou and Paul Purdon Martin}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2005}, volume={2006}, pages={P06004 - P06004} }

Motivated by a study of the crossing symmetry of the asymmetric twin or ‘gemini’ representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to the Yang–Baxter equation satisfying the crossing condition (that is, integrable quantum spin chains). We show that every crossing representation of the Temperley–Lieb algebra appears in this construction, and in particular that this…

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## References

SHOWING 1-10 OF 73 REFERENCES

### One-boundary Temperley–Lieb algebras in the XXZ and loop models

- Mathematics
- 2005

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and…

### Hecke algebra solutions to the reflection equation

- Mathematics
- 1994

We construct solutions to Sklyanin's reflection equation in the case in which the bulk Yang-Baxter solution is of Hecke algebra type. Each solution constitutes an extension of the Hecke algebra…

### Quantum group symmetries and non-local currents in 2D QFT

- Mathematics, Physics
- 1991

We construct and study the implications of some new non-local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions, including the sine-Gordon…

### Quantum Groups

- Mathematics
- 1993

This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions…

### Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom

- Physics
- 2003

### Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

- Mathematics
- 2001

### Quantum Group Symmetry in sine-Gordon and Affine Toda Field Theories on the Half-Line

- Mathematics
- 2001

Abstract: We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the…

### Common structures between finite systems and conformal field theories through quantum groups

- Mathematics, Physics
- 1990